caustic

Generally spoken, a caustic 1) is
formed by an envelope of light rays from a point source, diverted by some
optical instrument. The source can be at finite distance (like a flame) or at
infinite distance (like the sun).

The catacaustic of the logarithmic spiral
is the
curve itself (with a light source in the asymptote of the spiral). For a cycloid this is half true:
for a cycloid arch, rays perpendicular to the x-axis result in two cycloid arches.

The caustic can be generalized for different refraction indices (n1,
n2) at the two sides (same and opposite side of S, in relation to the
tangent). This curve is called the anticaustic.
For n (n1/n2) = 1 the orthotomic results.
It is said that the orthotomic can be identified with a cyclic.